On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• Main Authors: Nowak, A., Stempak, K., Szarek, T.Z.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147861
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings / A. Nowak, K. Stempak, T.Z. Szarek // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 46 назв. — англ.

We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to Zd2. Noteworthy, we admit negative values of the multiplicity functions. Our investigations include maximal operators, g-fu...